Sharada Nandan Raw

Restoration and recovery of damaged eco-epidemiological systems: Application to the Salton Sea, California, USA

In this paper, we have proposed and analysed a mathematical model to figure out possible ways to rescue a damaged eco-epidemiological system. Our strategy of rescue is based on the realization of the fact that chaotic dynamics often associated with excursions of system dynamics to extinction-sized densities. Chaotic dynamics of the model is depicted by 2D scans, bifurcation analysis, largest Lyapunov exponent and basin boundary calculations. 2D scan results show that μ, the total death rate of infected prey should be brought down in order to avoid chaotic dynamics. We have carried out linear and nonlinear stability analysis and obtained Hopf-bifurcation and persistence criteria of the proposed model system. The other outcome of this study is a suggestion which involves removal of infected fishes at regular interval of time. The estimation of timing and periodicity of the removal exercises would be decided by the nature of infection more than anything else. If this suggestion is carefully worked out and implemented, it would be most effective in restoring the health of the ecosystem which has immense ecological, economic and aesthetic potential. We discuss the implications of this result to Salton Sea, California, USA. The restoration of the Salton Sea provides a perspective for conservation and management strategy.

Incidence of Thalassemia and Sickle Cell Disease in Chhattisgarh, Central India:Using Hardy-Weinberg Equations

Thalassemia and Sickle Cell Disease (SCD) both are genetic blood disorders occurring by destruction in red blood cells (RBCs). Every year about 300,000 infants worldwide are born with Thalassemia syndrome (30 per cents) and sickle cell anaemia (70 per cents. Globally, the percentage of carriers of Thalassemia is greater than that of carriers of SCA, but because of the high frequency of the sickle cell gene in certain regions the number of affected births is higher than with Thalassemia. Due to a large population, and same blood, marriage in many communities, there is always a high chance of genetic disorders in Chhattisgarh which is one of the growing states of India. The incidence of genetic blood diseases in Chhattisgarh is considered high. According to the screened population, it is observed that the prevalence of SCD was 2.1%, sickle cell trait was 10% among different tribes. Also Thalassemia gene is prevalent in different Here we are describing the challenges, including lack of knowledge about genetic disease and less facility faced by parents in the Chhattisgarh his children affected by Thalassemia and SCD. We use Hardy-Weinberg equilibrium (HWE), a genetic approach for the prediction of allelic frequencies of SCD and Thalassemia. The aim of this study is to generate carrier frequencies of both the disease using HWE and accepting a number of resources which are useful for the eradication of SCD and Thalassemia from the affected population group.

Deterministic Chaos Versus Stochastic Oscillation in a Prey-Predator-Top Predator Model

Abstract The main objective of the present paper is to consider the dynamical analysis of a three dimensional prey-predator model within deterministic environment and the influence of environmental driving forces on the dynamics of the model system. For the deterministic model we have obtained the local asymptotic stability criteria of various equilibrium points and derived the condition for the existence of small amplitude periodic solution bifurcating from interior equilibrium point through Hopf bifurcation. We have obtained the parametric domain within which the model system exhibit chaotic oscillation and determined the route to chaos. Finally, we have shown that chaotic oscillation disappears in presence of environmental driving forces which actually affect the deterministic growth rates. These driving forces are unable to drive the system from a regime of deterministic chaos towards a stochastically stable situation. The stochastic stability results are discussed in terms of the stability of first a...

Challenges of living in the harsh environments: A mathematical modeling study

Abstract We propose and analyze a mathematical model, which mimics community dynamics of plants and animals in harsh environments. The mathematical model exploits type IV functional responses whose idiosyncrasies have been recognized only in recent years. The interaction of the middle predator with the top predator is cast into Leslie–Gower scheme. Linear and non-linear stability analyses are performed to get an idea of the stability behavior of the model food chain. It turns out that carrying capacity of the prey and the immunity parameter of the middle predator are two crucial parameters governing the model. Availability of alternative food options to the generalist predator also plays a key role in deciding the model dynamics. Simulation runs performed on this model provide insight into population dynamics of monkeys of macaque family found in northern Japan. These monkeys are social animals which reproduce sexually. The characteristic feature of the model dynamics is that the generalist predator (macaque monkeys) is able to avoid impending extinction frequently and recovers at a rate which falsify threats from exogenous external forces; extreme weather conditions, etc.

Crisis-Limited Chaotic Dynamics in an Eco-epidemiological System of the Salton Sea

In this paper, we have proposed a new eco-epidemiological model of the Salton Sea with Holling type II & IV functional responses. Numerical results are presented in the form of phase portraits, 2D scans, bifurcation analysis and basin boundary calculations. By these we have concluded that model system depicts the short-term recurrent chaos (STRC) and argued that crisis-limited chaotic dynamics can be commonly found in model eco-epidemiological systems.

Instabilities and Patterns in Zooplankton-Phytoplankton Dynamics: Effect of Spatial Heterogeneity

In this paper, we have made an attempt to understand the instabilities and complex spatiotemporal patterns induced by spatial heterogeneity in a spatial Rosenzweig - McAurthur model for phytoplankton-zooplankton-fish interaction. We have examined the effect of heterogeneity, and fish predation on the stability of the model system. Based on these conditions and by performing a series of extensive simulations, we observed the irregular patterns in the presence of spatial heterogeneity and fish predation acts as a regularizing factor. Numerical simulation results reveal that the complex temporal dynamics in natural communities may arise through the spatial dimension. Spatially induced chaos may have an important role in spatial pattern generation in heterogeneous environments.